|Any suggestions on how to get rid of this weed without chemicals??|
|This is a terribly invasive weed and very difficult to eradicate without chemicals, unfortunately. You can try to dig it out (you will likely have to dig repeatedly until you get every bit of root or rhizome) and certainly do not let it set seed. Otherwise, application(s) of glyphosate is typically recommended. To minimize the amount of chemical used you can cut the plant down and then wipe it onto the cut stems. Here is a little more information about it you may find interesting.
Good luck with this noxious weed!